Genus 2 Curves Database Igusa CM Invariants Database Quartic CM Fields Database

A quartic CM field field K is represented by invariants [D,A,B], where K = Q[x]/(x4+Ax2+B), and D is the discriminant of the totally real quadratic subfield (hence A2-4B = m2D for some m).

Class number: [Non-normal] [Cyclic]

[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]
[25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48]
[49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64] [65] [66] [67] [68] [69] [70] [71] [72]
[73] [74] [75] [76] [77] [78] [79] [80] [81] [82] [83] [84] [85] [86] [87] [88] [89] [90] [91] [92] [93] [94] [95] [96]
[97] [98] [99] [100] [101] [102] [103] [104] [105] [106] [107] [108] [109] [110] [111] [112] [113] [114] [115] [116] [117] [118] [119] [120]
[121] [122] [123] [124] [125] [126] [127] [128] [129] [130] [131] [132] [133] [134] [135] [136] [137] [138] [139] [140] [141] [142] [143] [144]
[145] [146] [147] [148] [149] [150] [151] [152] [153] [154] [155] [156] [157] [158] [159] [160] [161] [162] [163] [164] [165] [166] [167] [168]
[169] [170] [171] [172] [173] [174] [175] [176] [177] [178] [179] [180] [181] [182] [183] [184] [185] [186] [187] [188] [189] [190] [191] [192]
[193] [194] [195] [196] [197] [198] [199] [200] [201] [202] [203] [204] [205] [206] [207] [208] [209] [210] [211] [212] [213] [214] [215] [216]
[217] [218] [219] [220] [221] [222] [223] [224] [225] [226] [227] [228] [229] [230] [231] [232] [233] [234] [235] [236] [237] [238] [239] [240]
[241] [242] [243] [244] [245] [246] [247] [248] [249] [250] [251] [252] [253] [254] [255] [256] [257] [258] [259] [260] [261] [262] [263] [264]
[265] [266] [267] [268] [269] [270] [271] [272] [273] [274] [275] [276] [277] [278] [279] [280] [281] [282] [283] [284] [285] [286] [287] [288]
[289] [290] [291] [292] [293] [294] [295] [296] [297] [298] [299] [300] [301] [302] [303] [304] [305] [306] [307] [308] [309] [310] [311] [312]
[313] [314] [315] [316] [317] [318] [319] [320] [321] [322] [323] [324] [325] [326] [327] [328] [329] [330] [331] [332] [333] [334] [335] [336]
[337] [338] [339] [340] [341] [342] [343] [344] [345] [346] [347] [348] [349] [350] [351] [352] [353] [354] [355] [356] [357] [358] [359] [360]
[361] [362] [363] [364] [365] [366] [367] [368] [369] [370] [371] [372] [373] [374] [375] [376] [377] [378] [379] [380] [381] [382] [383] [384]
[385] [386] [387] [388] [389] [390] [391] [392] [393] [394] [395] [396] [397] [398] [399] [400] [401] [402] [403] [404] [405] [406] [407] [408]
[409] [410] [411] [412] [413] [414] [415] [416] [417] [418] [419] [420] [421] [422] [423] [424] [425] [426] [427] [428] [429] [430] [431] [432]
[433] [434] [435] [436] [437] [438] [439] [440] [441] [442] [443] [444] [445] [446] [447] [448] [449] [450] [451] [452] [453] [454] [455] [456]
[457] [458] [459] [460] [461] [462] [463] [464] [465] [466] [467] [468] [469] [470] [471] [472] [473] [474] [475] [476] [477] [478] [479] [480]
[481] [482] [483] [484] [485] [486] [487] [488] [489] [490] [491] [492] [493] [494] [495] [496] [497] [498] [499] [500] [501] [502] [503] [504]
[505] [506] [507] [508] [509] [510] [511] [512] [513] [514] [515] [516] [517] [518] [519] [520] [521] [522] [523] [524] [525] [526] [527] [528]
[529] [530] [531] [532] [533] [534] [535] [536] [537] [538] [539] [540] [541] [542] [543] [544] [545] [546] [547] [548] [549] [550] [551] [552]
[553] [554] [555] [556] [557] [558] [559] [560] [561] [562] [563] [564] [565] [566] [567] [568] [569] [570] [571] [572] [573] [574] [575] [576]

Class group C3 x C153 non-normal (D4) quartic CM field invariants: 198 fields

K Quartic invariants Cl(OK) Igusa invariants Kr Reflex invariants Cl(OKr) Igusa invariants
1) [5, 8654, 18690929] C3 x C153 ---) [18690929, 4327, 8000] C3 x C3 x C153
2) [5, 8014, 15728369] C3 x C153 ---) [15728369, 4007, 81920] C3 x C765
3) [5, 8326, 17226889] C3 x C153 197) [17226889, 4163, 25920] C3 x C153
4) [5, 6166, 9187369] C3 x C153 194) [9187369, 3083, 79380] C3 x C153
5) [5, 7573, 14299301] C3 x C153 195) [14299301, 5461, 3880805] C3 x C153
6) [5, 8413, 16601861] C3 x C153 196) [16601861, 5141, 2457005] C3 x C153
7) [8, 2698, 1819409] C3 x C153 183) [1819409, 1349, 98] C3 x C153
8) [8, 2858, 1989553] C3 x C153 185) [1989553, 1429, 13122] C3 x C153
9) [13, 3678, 3381089] C3 x C153 ---) [3381089, 1839, 208] C3 x C1683
10) [13, 10373, 26881501] C3 x C153 ---) [26881501, 17909, 19699693] C3 x C3 x C153
11) [13, 9341, 21805117] C3 x C153 198) [21805117, 16181, 16394677] C3 x C153
12) [17, 2515, 1539652] C3 x C153 156) [384913, 2359, 1294992] C3 x C153
13) [37, 2430, 1360193] C3 x C153 178) [1360193, 1215, 29008] C3 x C153
14) [37, 1974, 687641] C3 x C153 167) [687641, 987, 71632] C3 x C153
15) [101, 1457, 499781] C3 x C153 162) [499781, 2914, 123725] C3 x C153
16) [137, 1199, 358544] C3 x C153 123) [22409, 1571, 342500] C3 x C153
17) [137, 5446, 3907529] C3 x C153 ---) [3907529, 2723, 876800] C3 x C9 x C153
18) [137, 5030, 3791273] C3 x C153 192) [3791273, 2515, 633488] C3 x C153
19) [157, 2717, 1743433] C3 x C153 182) [1743433, 5434, 408357] C3 x C153
20) [157, 2174, 1158961] C3 x C153 ---) [1158961, 1087, 5652] C3 x C3 x C153
21) [173, 1214, 357377] C3 x C153 154) [357377, 607, 2768] C3 x C153
22) [181, 1314, 396173] C3 x C153 ---) [396173, 657, 8869] C3 x C3 x C153
23) [193, 1970, 907693] C3 x C153 ---) [907693, 985, 15633] C3 x C3 x C153
24) [229, 1838, 20161] C3 x C153 ---) [20161, 919, 206100] C153
25) [233, 4102, 1686473] C3 x C153 181) [1686473, 2051, 630032] C3 x C153
26) [233, 1010, 246637] C3 x C153 149) [246637, 505, 2097] C3 x C153
27) [241, 2210, 1142941] C3 x C153 171) [1142941, 1105, 19521] C3 x C153
28) [241, 3214, 1040049] C3 x C153 140) [115561, 1607, 385600] C3 x C153
29) [257, 1222, 307529] C3 x C153 150) [307529, 611, 16448] C3 x C153
30) [257, 838, 159113] C3 x C153 ---) [159113, 419, 4112] C153
31) [509, 653, 103421] C3 x C153 ---) [103421, 1306, 12725] C3 x C1071
32) [569, 2966, 1616633] C3 x C153 ---) [1616633, 1483, 145664] C3 x C3 x C153
33) [661, 1978, 658197] C3 x C153 137) [73133, 989, 79981] C3 x C153
34) [673, 650, 102933] C3 x C153 108) [11437, 325, 673] C3 x C153
35) [677, 989, 60217] C3 x C153 133) [60217, 1978, 737253] C3 x C153
36) [733, 306, 20477] C3 x C153 ---) [20477, 153, 733] C153
37) [761, 3387, 1854100] C3 x C153 120) [18541, 3365, 1157481] C3 x C153
38) [1129, 706, 11709] C3 x C153 ---) [1301, 353, 28225] C51
39) [1129, 442, 44325] C3 x C153 ---) [197, 221, 1129] C51
40) [1373, 1966, 614801] C3 x C153 77) [5081, 983, 87872] C3 x C153
41) [1489, 551, 45748] C3 x C153 ---) [11437, 1102, 120609] C153
42) [1613, 697, 88789] C3 x C153 139) [88789, 1394, 130653] C3 x C153
43) [1901, 745, 1409] C3 x C153 ---) [1409, 1490, 549389] C153
44) [1901, 1014, 226633] C3 x C153 ---) [1873, 507, 7604] C153
45) [2213, 226, 3917] C3 x C153 ---) [3917, 113, 2213] C153
46) [2213, 3274, 1962757] C3 x C153 ---) [5437, 1637, 179253] C153
47) [2557, 473, 4153] C3 x C153 ---) [4153, 946, 207117] C153
48) [2557, 2025, 993833] C3 x C153 ---) [2753, 2655, 1728532] C153
49) [2557, 3405, 2821157] C3 x C153 81) [5333, 2133, 432133] C3 x C153
50) [2677, 681, 2837] C3 x C153 ---) [2837, 1362, 452413] C153
51) [2677, 1258, 299269] C3 x C153 ---) [829, 629, 24093] C153
52) [2777, 4395, 496192] C3 x C153 97) [7753, 2531, 1599552] C3 x C153
53) [2789, 1086, 250225] C3 x C153 104) [10009, 543, 11156] C3 x C153
54) [2857, 287, 14164] C3 x C153 ---) [3541, 574, 25713] C153
55) [2917, 93, 1433] C3 x C153 ---) [1433, 186, 2917] C153
56) [3109, 6181, 9376309] C3 x C153 107) [11149, 3601, 2614669] C3 x C153
57) [3137, 743, 99584] C3 x C153 ---) [389, 1117, 78425] C51
58) [3221, 3830, 368921] C3 x C153 ---) [7529, 1915, 824576] C153
59) [3221, 1049, 139013] C3 x C153 ---) [2837, 2098, 544349] C153
60) [3389, 2137, 693497] C3 x C153 112) [14153, 4274, 1792781] C3 x C153
61) [3389, 145, 4409] C3 x C153 ---) [4409, 290, 3389] C3 x C9 x C153
62) [3541, 6837, 9730625] C3 x C153 116) [15569, 4047, 354100] C3 x C153
63) [3761, 1387, 66292] C3 x C153 118) [16573, 2774, 1658601] C3 x C153
64) [3821, 5974, 7943993] C3 x C153 114) [15017, 2987, 244544] C3 x C153
65) [3889, 7582, 3855825] C3 x C153 ---) [17137, 3791, 2628964] C153
66) [4133, 3662, 2294513] C3 x C153 ---) [13577, 1831, 264512] C3 x C3 x C153
67) [4349, 209, 9833] C3 x C153 ---) [9833, 418, 4349] C3 x C3 x C153
68) [4409, 2091, 33808] C3 x C153 ---) [2113, 2539, 634896] C51
69) [4481, 3019, 207248] C3 x C153 ---) [12953, 6038, 8285369] C153
70) [4493, 2293, 819109] C3 x C153 ---) [2269, 2253, 220157] C153
71) [4621, 733, 123925] C3 x C153 76) [4957, 1466, 41589] C3 x C153
72) [4729, 3171, 1888400] C3 x C153 ---) [4721, 4899, 1891600] C153
73) [4793, 1203, 15508] C3 x C153 ---) [3877, 2406, 1385177] C3 x C3 x C153
74) [4933, 305, 12157] C3 x C153 ---) [12157, 610, 44397] C153
75) [4933, 473, 25101] C3 x C153 ---) [2789, 946, 123325] C153
76) [4957, 1466, 41589] C3 x C153 71) [4621, 733, 123925] C3 x C153
77) [5081, 983, 87872] C3 x C153 40) [1373, 1966, 614801] C3 x C153
78) [5101, 4617, 4960625] C3 x C153 99) [7937, 5343, 5896756] C3 x C153
79) [5261, 3330, 2751181] C3 x C153 ---) [7621, 1665, 5261] C153
80) [5261, 113, 1877] C3 x C153 ---) [1877, 226, 5261] C153
81) [5333, 2133, 432133] C3 x C153 49) [2557, 3405, 2821157] C3 x C153
82) [5381, 5290, 3358469] C3 x C153 ---) [11621, 2645, 909389] C3 x C1071
83) [5413, 1686, 364217] C3 x C153 96) [7433, 843, 86608] C3 x C153
84) [5437, 5401, 440721] C3 x C153 86) [5441, 5299, 543700] C3 x C153
85) [5437, 2398, 45729] C3 x C153 ---) [5081, 1199, 347968] C3 x C3 x C153
86) [5441, 5299, 543700] C3 x C153 84) [5437, 5401, 440721] C3 x C153
87) [5477, 2393, 827773] C3 x C153 ---) [2293, 2625, 662717] C153
88) [5557, 2494, 132417] C3 x C153 113) [14713, 1247, 355648] C3 x C153
89) [5573, 5342, 2765009] C3 x C153 117) [16361, 2671, 1092308] C3 x C153
90) [5701, 7734, 13494233] C3 x C153 103) [9857, 3867, 364864] C3 x C153
91) [5741, 2181, 1015525] C3 x C153 ---) [829, 1265, 51669] C153
92) [5741, 718, 37025] C3 x C153 ---) [1481, 359, 22964] C153
93) [5821, 6173, 2598037] C3 x C153 ---) [15373, 7409, 12858589] C153
94) [5981, 11833, 16581997] C3 x C153 121) [19717, 6073, 9097101] C3 x C153
95) [6997, 837, 173393] C3 x C153 ---) [1433, 1674, 6997] C153
96) [7433, 843, 86608] C3 x C153 83) [5413, 1686, 364217] C3 x C153
97) [7753, 2531, 1599552] C3 x C153 52) [2777, 4395, 496192] C3 x C153
98) [7873, 311, 22212] C3 x C153 ---) [617, 622, 7873] C51
99) [7937, 5343, 5896756] C3 x C153 78) [5101, 4617, 4960625] C3 x C153
100) [8069, 2218, 939397] C3 x C153 ---) [1117, 1109, 72621] C153
101) [9749, 1445, 519569] C3 x C153 ---) [281, 1003, 38996] C153
102) [9749, 2669, 257609] C3 x C153 ---) [2129, 4079, 1910804] C153
103) [9857, 3867, 364864] C3 x C153 90) [5701, 7734, 13494233] C3 x C153
104) [10009, 543, 11156] C3 x C153 53) [2789, 1086, 250225] C3 x C153
105) [10069, 3489, 2980349] C3 x C153 ---) [1061, 2261, 1218349] C153
106) [10069, 1485, 427961] C3 x C153 ---) [809, 2807, 1006900] C153
107) [11149, 3601, 2614669] C3 x C153 56) [3109, 6181, 9376309] C3 x C153
108) [11437, 325, 673] C3 x C153 34) [673, 650, 102933] C3 x C153
109) [11789, 870, 601] C3 x C153 ---) [601, 435, 47156] C153
110) [12269, 1538, 149677] C3 x C153 ---) [1237, 769, 110421] C153
111) [12409, 2090, 645301] C3 x C153 ---) [349, 1045, 111681] C51
112) [14153, 4274, 1792781] C3 x C153 60) [3389, 2137, 693497] C3 x C153
113) [14713, 1247, 355648] C3 x C153 88) [5557, 2494, 132417] C3 x C153
114) [15017, 2987, 244544] C3 x C153 64) [3821, 5974, 7943993] C3 x C153
115) [15349, 5045, 2184241] C3 x C153 ---) [4129, 6827, 1534900] C153
116) [15569, 4047, 354100] C3 x C153 62) [3541, 6837, 9730625] C3 x C153
117) [16361, 2671, 1092308] C3 x C153 89) [5573, 5342, 2765009] C3 x C153
118) [16573, 2774, 1658601] C3 x C153 63) [3761, 1387, 66292] C3 x C153
119) [17581, 2794, 193509] C3 x C153 ---) [2389, 1397, 439525] C153
120) [18541, 3365, 1157481] C3 x C153 37) [761, 3387, 1854100] C3 x C153
121) [19717, 6073, 9097101] C3 x C153 94) [5981, 11833, 16581997] C3 x C153
122) [20521, 1451, 110800] C3 x C153 ---) [277, 2021, 1005529] C153
123) [22409, 1571, 342500] C3 x C153 16) [137, 1199, 358544] C3 x C153
124) [24281, 1787, 792272] C3 x C153 ---) [293, 1993, 24281] C153
125) [24697, 1555, 301968] C3 x C153 ---) [233, 1851, 395152] C51
126) [25469, 161, 113] C3 x C153 ---) [113, 322, 25469] C153
127) [34877, 1421, 426337] C3 x C153 ---) [193, 2615, 1255572] C153
128) [35597, 2182, 620729] C3 x C153 ---) [281, 1091, 142388] C153
129) [38993, 271, 8612] C3 x C153 ---) [2153, 542, 38993] C765
130) [40361, 595, 78416] C3 x C153 ---) [29, 985, 40361] C51
131) [45641, 866, 4925] C3 x C153 ---) [197, 433, 45641] C153
132) [59209, 1231, 8784] C3 x C153 ---) [61, 1585, 532881] C51
133) [60217, 1978, 737253] C3 x C153 35) [677, 989, 60217] C3 x C153
134) [61961, 259, 1280] C3 x C153 ---) [5, 518, 61961] C51
135) [64013, 1066, 28037] C3 x C153 ---) [53, 533, 64013] C51
136) [71161, 427, 27792] C3 x C153 ---) [193, 854, 71161] C51
137) [73133, 989, 79981] C3 x C153 33) [661, 1978, 658197] C3 x C153
138) [85313, 2151, 111616] C3 x C153 ---) [109, 2889, 85313] C153
139) [88789, 1394, 130653] C3 x C153 42) [1613, 697, 88789] C3 x C153
140) [115561, 1607, 385600] C3 x C153 28) [241, 3214, 1040049] C3 x C153
141) [155537, 3166, 17297] C3 x C153 ---) [353, 1583, 622148] C153
142) [167537, 839, 134096] C3 x C153 ---) [29, 1678, 167537] C153
143) [169097, 675, 71632] C3 x C153 ---) [37, 1350, 169097] C153
144) [190093, 601, 42777] C3 x C153 ---) [97, 1202, 190093] C153
145) [190093, 673, 65709] C3 x C153 ---) [149, 1346, 190093] C153
146) [190577, 437, 98] C3 x C153 ---) [8, 874, 190577] C153
147) [190753, 525, 21218] C3 x C153 ---) [8, 1050, 190753] C153
148) [203393, 1475, 86272] C3 x C153 ---) [337, 2950, 1830537] C153
149) [246637, 505, 2097] C3 x C153 26) [233, 1010, 246637] C3 x C153
150) [307529, 611, 16448] C3 x C153 29) [257, 1222, 307529] C3 x C153
151) [310181, 557, 17] C3 x C153 ---) [17, 1114, 310181] C153
152) [310901, 701, 45125] C3 x C153 ---) [5, 1153, 310901] C51
153) [342233, 4163, 140288] C3 x C153 ---) [137, 5987, 5475728] C153
154) [357377, 607, 2768] C3 x C153 21) [173, 1214, 357377] C3 x C153
155) [364241, 695, 29696] C3 x C153 ---) [29, 1390, 364241] C153
156) [384913, 2359, 1294992] C3 x C153 12) [17, 2515, 1539652] C3 x C153
157) [396373, 637, 2349] C3 x C153 ---) [29, 1274, 396373] C153
158) [417737, 745, 34322] C3 x C153 ---) [8, 1490, 417737] C51
159) [420361, 859, 79380] C3 x C153 ---) [5, 1317, 420361] C153
160) [425641, 979, 133200] C3 x C153 ---) [37, 1958, 425641] C153
161) [466033, 855, 66248] C3 x C153 ---) [8, 1710, 466033] C153
162) [499781, 2914, 123725] C3 x C153 15) [101, 1457, 499781] C3 x C153
163) [531457, 2435, 286528] C3 x C153 ---) [37, 4417, 4783113] C153
164) [534841, 779, 18000] C3 x C153 ---) [5, 1558, 534841] C153
165) [662177, 2675, 299008] C3 x C153 ---) [73, 5350, 5959593] C153
166) [663529, 947, 58320] C3 x C153 ---) [5, 1761, 663529] C153
167) [687641, 987, 71632] C3 x C153 14) [37, 1974, 687641] C3 x C153
168) [812081, 1031, 62720] C3 x C153 ---) [5, 1973, 812081] C153
169) [924661, 1341, 218405] C3 x C153 ---) [5, 1933, 924661] C153
170) [1017061, 1509, 315005] C3 x C153 ---) [5, 2017, 1017061] C153
171) [1142941, 1105, 19521] C3 x C153 27) [241, 2210, 1142941] C3 x C153
172) [1151221, 1821, 541205] C3 x C153 ---) [5, 2173, 1151221] C153
173) [1229461, 1821, 521645] C3 x C153 ---) [5, 2233, 1229461] C153
174) [1232617, 1843, 541008] C3 x C153 ---) [13, 3686, 1232617] C153
175) [1265321, 1139, 8000] C3 x C153 ---) [5, 2278, 1265321] C153
176) [1268233, 1283, 94464] C3 x C153 ---) [41, 2566, 1268233] C153
177) [1280737, 1135, 1872] C3 x C153 ---) [13, 2270, 1280737] C153
178) [1360193, 1215, 29008] C3 x C153 13) [37, 2430, 1360193] C3 x C153
179) [1440953, 1483, 189584] C3 x C153 ---) [41, 2966, 1440953] C153
180) [1450489, 1483, 187200] C3 x C153 ---) [13, 2966, 1450489] C153
181) [1686473, 2051, 630032] C3 x C153 25) [233, 4102, 1686473] C3 x C153
182) [1743433, 5434, 408357] C3 x C153 19) [157, 2717, 1743433] C3 x C153
183) [1819409, 1349, 98] C3 x C153 7) [8, 2698, 1819409] C3 x C153
184) [1855741, 2761, 1441845] C3 x C153 ---) [5, 2913, 1855741] C153
185) [1989553, 1429, 13122] C3 x C153 8) [8, 2858, 1989553] C3 x C153
186) [2055769, 2363, 882000] C3 x C153 ---) [5, 2889, 2055769] C153
187) [2311193, 1531, 8192] C3 x C153 ---) [8, 3062, 2311193] C153
188) [2318153, 1891, 314432] C3 x C153 ---) [17, 3782, 2318153] C153
189) [2344409, 2867, 1468820] C3 x C153 ---) [5, 3181, 2344409] C153
190) [2702789, 2837, 1336445] C3 x C153 ---) [5, 3341, 2702789] C153
191) [3757673, 1939, 512] C3 x C153 ---) [8, 3878, 3757673] C153
192) [3791273, 2515, 633488] C3 x C153 18) [137, 5030, 3791273] C3 x C153
193) [4138601, 2035, 656] C3 x C153 ---) [41, 4070, 4138601] C153
194) [9187369, 3083, 79380] C3 x C153 4) [5, 6166, 9187369] C3 x C153
195) [14299301, 5461, 3880805] C3 x C153 5) [5, 7573, 14299301] C3 x C153
196) [16601861, 5141, 2457005] C3 x C153 6) [5, 8413, 16601861] C3 x C153
197) [17226889, 4163, 25920] C3 x C153 3) [5, 8326, 17226889] C3 x C153
198) [21805117, 16181, 16394677] C3 x C153 11) [13, 9341, 21805117] C3 x C153